Solomon Ortwer Adee

Verified

Solomon verified their affiliation via an institutional email.

Learn more

Verified

Solomon verified their affiliation via an institutional email.

Learn more

• BSc, MSc, PhD
• Professor (Associate) at Modibbo Adama University of Technology

In this research work, the extended Backward Differentiation Formula (EBDF) is used to develop an embedded block hybrid method (EBHM) for step numbers k=5 and 6 for the solution of first-order initial-value problems (IVPs) in ordinary differential equations (ODEs). The methods are obtained by continuous approximation using multi-step collocation te...

In this research, polynomial collocation method was used to develop and implement numerical solutions of nonlinear two-dimensional (2D) mixed Volterra-Fredholm integral equations. The Integral equation was transform into systems of algebraic equations using standard collocation points with Bernstein polynomial as a basis function and then solves th...

This study uses finite power series as the basis function and interpolation and collocation techniques to study a class of implicit block methods of a seventh-derivative type. Discrete schemes are implicit two-point block methods that are obtained by selecting collocation points carefully and unevenly in order to improve the stability of the method...

The Malthusian population model and Susceptible-Infectious-Recovered (SIR) epidemic model are described by systems of first order ordinary differential equations (ODEs) that model the dynamics of population growth and infectious disease spread respectively. Efficient numerical methods to solve these models play an integral role across mathematical...

In this paper, we utilized the linear generalized inverse multiquadric function and the quadratic generalized multiquadric function as radial basis functions for the quadrature-based projection method in solving Volterra integro-differential equations (VIDE) of first and second orders. The selected examples are evaluated using MAPLE 17 and MATLAB S...

We use the multistep collocation technique to derive a pair of two-step block hybrid methods incorporating two off-step interpolation points and one off-step collocation point. The block hybrid methods are then reformulated into a pair of new sixth-stage implicit Runge-Kutta-type methods, which are implemented in solving first-order ordinary differ...

A single-step modified block hybrid method (MBHM) of order five for solving the general second-order initial-value problems (IVPs) of ordinary differential equations (ODEs) is derived through a multistep collocation approach. Basic convergence properties of the new method are established, and its numerical accuracy is illustrated using numerical ex...

In this research we formulated the Plants diseases model with the aim of studying the dynamics of the use of lysobacter antibioticus for prevention and control of rice bacterial blight. The disease free equilibrium state of the models was also obtained by equating each of the equation of the modified model to zero and simplifying. The basic reprodu...

In this paper, we derive some new k-step hybrid block methods (HBM) for the solution of first-order non-stiff initial value problems (IVPs) of ordinary differential equations (ODEs). A continuous hybrid multistep method (CHM) with variable coefficients is first developed using interpolation and collocation of a polynomial approximate solution. Disc...

We propose a new hybrid method by embedding the extended four-step backward differentiation formulae of Akinfenwa & Jator (2015) into a one-step method by a continuous approximation via multistep collocation technique for the solution of first-order stiff initial value problems of ordinary differential equations. The embedded hybrid block method (E...

In this research, we constructed collocation methods for approximating the solutions of Volterra integro-differential equations using Bernoulli polynomials and Euler polynomials as basic functions. Sample problems ranging from linear first to second order Volterra integro-differential (VIDEs) equations using the methods developed were solved. The m...

We present a single-step block hybrid method obtained through multistep collocation (MC) approach, by incorporating three off-grid interpolation and two off-grid collocation points in a continuous linear hybrid method as opposed to a similar work where two-step methods were obtained. The discrete hybrid methods are used in the formulation a block m...

A new higher-implicit block method for the direct numerical solution of fourth order ordinary differential equation is derived in this research paper. The formulation of the new formula which is 15-step, is achieved through interpolation and collocation techniques. The basic numerical properties of the method such as zero-stability, consistency and...

Two numerical methods- I2BBDF2 and I22BBDF2 that compute two points simultaneously at every step of integration by first providing a starting value via fourth order Runge-Kutta method are derived using Taylor series expansion. The two-point block schemes are derived by modifying the existing I2BBDF (5) method of Mohamad et al., (2018). Convergence...

Radial basis function method of lines (RBF-MOLs) for approximating the two-dimensional heat equation were formulated using two globally supported and positive radial basis functions (RBFs), namely, inverse quadratic (IQ), generalized inverse multiquadric (GIMQ) and the fourth order Runge-Kutta method. The RBFs were used for discretizing the space v...

Globally supported radial basis functions (RBFs) arc mcshless methods that use information from every centre in the domain to approximate a function value or derivative at a single point. They arc highly accurate methods that are used for the approximation of multivariate scattered data and often converge exponentially. On the other hand, positive...

This work explores the Julia and Mandelbrot sets of the Gamma function by extending the function to the entire complex plane through analytic continuation and functional equations. Various Julia and Mandelbrot sets associated with the Gamma function are generated using the iterative function f (z) = (z) λ Γ + λ , with different parameter λ − values...

In this paper, we present a block method for the direct solution of third order initial value problems of ordinary differential equations. Collocation and interpolation approach was adopted to generate a continuous linear multistep method which was then solved for the independent solution to give a continuous block method. We evaluated the result a...

A block method for solution of third order initial value problems of ordinary differential equations is presented in this paper. The scheme was derived using collocation and interpolation approach to generate a continuous linear multistep method which was solved for the independent solution to give a continuous block method. The result was evaluate...

A new three and five step block linear methods based on the Adams family for the direct solution of stiff initial value problems (IVPs) are proposed. The main methods together with the additional methods which constitute the block methods are derived via interpolation and collocation procedures. These methods are of uniform order four and six for t...

A two step block hybrid Adam Moulton method of uniform order five is presented for the solution of stiff initial value problems. The individual schemes that made up the block method are obtained from the same continuous scheme which is applied to provide the solutions of stiff initial value problems on non overlapping intervals. The constructed blo...

The authors report a hybrid formula of order four for starting the Numerov method applied to the initial-value problem for y '' =f(x,y), over the recently obtained result of order three by P. Onumanyi, U. W. Sirisena and S. O. Adee [Some theoretical considerations of continuous of continuous linear multistep methods for u (v) =f(x,u), v=1,2, Bagale...

A class of methods for the numerical solution of initial value problems whose solution has singular point(s) shall be discussed. They are A- and L-stable and were found to perform efficiently well when faced with singularity problem but perform poorly when applied to non-singular problems.

We discuss some theory, which are of immense importance to the study and application of the continuous linear multistep method (CLMM) developed in earlier works for the first and special second order systems of ordinary differential equations (ODEs). The main results are as follows: (i) The associated matrix M is shown to be non-singular and a new...